A risk people take by putting themselves out there to show how you feel for your significant other, usually when doubt is cast against your feelings. The "grand gesture" usually entails giving up something big in exchange for the gratitude and love of your significant other.

I showed Amy how much I love her want to be with her with my grand gesture of quitting my job in LA to be with her in New York.

John Cusak holding a boombox above his head all night to prove his dedication to Ione Sky in 'Say Anything.'